Answer with Step-by-step explanation:
We have to find the solution of the equation:
[tex]x^4+6x^2+5=0[/tex]
Let u=x²
Then, above equation is transformed to:
[tex]u^2+6u+5=0[/tex]
it could also be written as:
[tex]u^2+5u+u+5=0[/tex]
u(u+5)+1(u+5)=0
(u+1)(u+5)=0
either u+1=0 or u+5=0
either u= -1 or u= -5
Putting u=x²
x² = -1 or x² = -5
On taking square root both sides
x= ± i or x= ± i√5
Hence, roots of the equation [tex]x^4+6x^2+5=0[/tex] are:
i , -i , i√5 and -i√5
